All categories

3 years ago

Given ABE is an isosceles triangle with ZABE - 100° and AMNP is an isosceles triangle with one base angle measuring 40°. Are

Mathematics

1 answer:

MrMuchimi3 years ago

8 0

Two triangle ABE and MNP are similar by AA criterion

Step-by-step explanation:

Given that ABE is an isosceles Δ with ABE= 100°

this means that some of the other two angles must be =180°-100°=80°

Since the triangle is an isosceles Δ meaning two sides measure must be equal, it means the other two sides measure 40° each.

∠BAC=∠ACB=40°

In MNP one of the base angles is 40° and the triangle is isosceles. For an isosceles triangle base angles are always equal hence other base angle is also 40° meaning

the angle measures come out to be 40°,40° and 100°

Since all the angle measures are same the two triangles are similar in aspect by AA criterion where AA refers to "angle-angle"

You might be interested in

The table shows the estimated number of bees, y, in a hive x days after a pesticide is released near the hive.

Oksana_A [137]

Answer:

Step-by-step explanation:

The given table is

Days Bees

0 10,000

10 7,500

20 5,600

30 4,200

40 3,200

50 2,400

Where $x$ represents days and $y$ represents bees.

The exponential function that models this problem must be like

$y=a(1-r)^{x}$ , which represenst an exponential decary, because in this case, the number of bees decays.

We nned to use one points, to find the rate of decay. We know that $a=10,000$ , because it starts with 10,000 bees.

Let's use the points (10, 7500)

$y=a(1-r)^{x}\\7500=10000(1-r)^{10}$

Solving for $r$ , we have

$\frac{7500}{10000}=(1-r)^{10} \\(1-r)^{10} =0.75$

Using logarithms, we have

$ln((1-r)^{10}) =ln(0.75)\\10 \times ln(1-r)=ln(0.75)\\ln(1-r)=\frac{ln(0.75)}{10} \approx -0.03\\e^{ln(1-r)}=e^{-0.03}\\1-r =e^{-0.03}\\r=-e^{-0.03}+1 \approx 1.97$

Replacing all values in the model, we have

$y=10000(1-1.97)^{x}\\y=10000(0.97)^{x}$

Therefore, the right answer is the first choice, that's the best approximation to this situation.

6 0

2 years ago

Read 2 more answers

John spends 1 hour making birthday cards. If each birthday card takes 3 minutes to make, how many birthday cards can John make?

GuDViN [60]

John can make 20 cards

3 0

3 years ago

Read 2 more answers

What 2 numbers multiply to -36 and add to 16

KatRina [158]

Answer:

Step-by-step explanation:

I understand

6 0

3 years ago

Ok, so I gotta find the area for these rooms, but its not clear where the rooms end.. Where would you guys say the living room e

notsponge [240]

Measure your foot size then go to the wall barefooted and walk in a straight line to the door the wall to wall the against the wall then add

8 0

3 years ago

Read 2 more answers

Help with these two math questions please

Furkat [3]

Because the two triangles are similar, their angles will be the exact same.

Therefore, Angle B is 130 degrees

The answer is D.

There isn't a graph to look at for the second question so I can't help you on that one

3 0

3 years ago

Read 2 more answers